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Locke, Arnauld, and Abstract Ideas* Kenneth L Locke, Arnauld, and Abstract Ideas* Kenneth L. Pearce Trinity College Dublin A great deal of the criticism directed at John Locke’s theory of abstract ideas, including George Berkeley’s famous critique (PHK, Intro §§7–21), 1 assumes that a Lockean abstract idea is a special kind of idea which by its very nature either represents many diverse particulars or represents separately things that cannot exist in separation (see PHK, Intro §10).2 I will call this the intrinsic theory of abstraction, since it holds that abstract ideas differ intrinsically from concrete (i.e., non-abstract) ideas. The claim that Locke held the intrinsic theory has been challenged by scholars such as Kenneth Winkler and Michael Ayers who regard it as uncharitable to Locke in light of the obvious problems faced by this theory of abstraction. Winkler and Ayers argue that Locke held instead that to have an abstract idea is to attend selectively to some portion of the content of a particular idea. On this view, to have an abstract idea is not to have a special kind of idea but to have an ordinary idea in a special way. I will call this the extrinsic theory of abstraction, since it holds that ideas are not intrinsically abstract but rather are abstract in virtue of the manner in which they are had (perceived). According to Ayers, this interpretation is contextually plausible since Locke was greatly influenced by Antoine Arnauld, and Arnauld endorsed the extrinsic theory of abstraction. I argue, on the contrary, that both Arnauld and Locke endorse the intrinsic theory. I begin, in §1, with a more careful definition of the difference between the intrinsic and extrinsic theories of abstraction. In §2 I show that, despite Arnauld’s talk about selective attention, Arnauld holds the intrinsic theory. In §3, I show that a consistent interpretation of Locke’s remarks on abstract ideas can be developed on the assumption that Locke did indeed follow Arnauld in this. Thus, contrary to Winkler and Ayers, both textual and contextual evidence favors the attribution of the intrinsic theory to Locke. In §4, I address the argument from interpretive charity against the attribution of the intrinsic theory to * Forthcoming in British Journal for the History of Philosophy. Accepted 26 June, 2018. 1 Although Berkeley makes this assumption, it is unclear what role, if any, it plays in his argument. See, e.g., Bolton 1987; Winkler 1989, ch. 2; Pappas 2000, ch. 3; Pearce 2017, 15–29. I am here focused on the interpretation of Locke and Arnauld, and will therefore not be addressing this question. 2 In the secondary literature on Berkeley, these two kinds of abstraction have been dubbed ‘generalizing abstraction’ and ‘singling abstraction’. See Rickless 2012. A predecessor of this distinction can be found in the Port-Royal Logic’s distinction between four kinds of “knowledge by parts,” three of which are said to be species of abstraction (Logic, 37–38). Varieties 2 and 3 are kinds of singling abstraction, the fourth and final variety is generalizing abstraction. 1 Locke. I provide a threefold response to this argument: first, although my interpretation does recognize a tension in Locke’s thought, it does not attribute any obvious incoherence to him. Second, Locke might well regard attempts to remove this tension as violating the principles of his “Historical, plain Method” (EHU, §1.1.2). Third and finally, the tension in question can plausibly be seen as arising from Locke’s attempt to adapt the Cartesian logic of Port-Royal to an empiricist philosophy of ideas. I conclude that considerations of charity do not outweigh the textual and contextual evidence: Locke’s process of abstraction produces special ideas of a peculiar and problematic sort. 1 Intrinsic and Extrinsic Theories of Abstraction According to intrinsic theories of abstraction, abstract ideas differ intrinsically from concrete ideas. In other words, the intrinsic theory holds that an abstract idea is an idea of a special kind while the extrinsic theory holds that an abstract idea is merely an ordinary idea had in a special way. The distinction between intrinsic and extrinsic theories of abstraction should be distinguished from the debate over what Winkler calls ‘the content assumption’ about ideas. According to the content assumption, “the content of thought is determined by its object” (Winkler 1989, 39). The content assumption is a component of one particular version of the intrinsic theory. On this view, ideas are the internal, immediate objects of thought and the intrinsic nature of the idea determines the content of thought. On such a view, abstract ideas must differ intrinsically from concrete ideas because they differ in content: the abstract idea apple is about apples in general, while a particular apple idea is about a particular apple. Winkler and Ayers hold that Locke rejects the content assumption and instead holds a version of the extrinsic theory.3 According to this view, as Winkler puts it, “we may be thinking of a particular triangle or of triangularity in general while confronting one and the same idea, depending on how much of the idea we attend to” (Winkler 1989, 39). Similarly, according to Ayers, “The abstract idea just is the phenomenal particular currently before the mind and representing all particulars which precisely resemble it in the respect upon which the mind is focused in abstraction” (Ayers 1991, 1:249). One reason it is important to distinguish the content assumption—a component of one particular version of the intrinsic theory—from the intrinsic theory more broadly, is that the version of the intrinsic theory that relies on the content assumption also contains a second assumption: that ideas are objects of thought. However, according to both Winkler and Ayers, Locke’s text contains an ambiguity between ideas considered as objects of thought and ideas as acts of thinking (Winkler 1989, 41–42; Ayers 1991, 1:56– 57). Further, Arnauld is often interpreted as taking ideas to be acts, rather than objects, of thought (see below, §2). The distinction between intrinsic and extrinsic theories of abstraction is, however, independent of the question of whether ideas are acts or objects: the intrinsic theory simply holds that an abstract idea is a special kind of idea, differing 3 Yaffe 2004 argues that Locke does endorse the content assumption as part of his general theory of ideas. 2 intrinsically from a concrete idea, while the extrinsic theory holds that one and the same idea may be either abstract or concrete depending on circumstances extrinsic to that idea. On the particular version of the extrinsic theory attributed to Locke by Winkler and Ayers, an abstract idea is just a concrete idea to which the mind attends selectively. In other words, to have an abstract idea is just to attend to some particular feature or features of a fully determinate concrete idea to the exclusion of its other features. I will now argue that both Arnauld and Locke held the intrinsic theory. 2 Arnauld on Abstraction That Arnauld held the intrinsic theory rather than the extrinsic theory of abstraction is apparent both from direct textual evidence and from systematic considerations. I begin with the textual evidence. In the Port-Royal Logic, Arnauld (with his collaborator Pierre Nicole), describes abstraction as follows: Suppose, for example, I reflect that I am thinking, and, in consequence, that I am the I who thinks. In my idea of the I who thinks, I can consider a thinking thing without noticing that it is I, although in me the I and the one who thinks are one and the same thing. The idea I thereby conceive of a person who thinks can represent not only me but all other thinking persons. By the same token, if I draw an equilateral triangle on a piece of paper, and if I concentrate on examining it on this paper along with all the accidental circumstances determining it, I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the thought that the triangle is a figure bounded by three equal lines, the idea I form will, on the one hand, represent more clearly the equality of lines and, on the other, be able to represent all equilateral triangles … Now in these abstractions it is clear that the lower degree includes the higher degree along with some particular determination, just as the I includes that which thinks, the equilateral triangle includes the triangle, and the triangle the straight-lined figure. But since the higher degree is less determinate, it can represent more things (Logic, 38, emphasis added).4 This text is quite explicit that selective attention results in the formation of a new idea. In the first example, I focus on myself qua thinking thing and thereby conceive a new idea that includes only this thinking, without my particularities, and is therefore suited to represent all thinking things. In the second example, I attend only to the fact that the thing in question “is a figure bounded by three equal lines” and thereby form a new idea containing only this content and therefore suited to represent all equilateral triangles. Additionally, according to this text, these abstractions form ideas that “can represent more things.” The concrete ideas with which we began are capable only of representing some particular individual. Abstraction forms new ideas capable of representing many individuals. This interpretation is confirmed at the beginning of the next chapter: 4 The account here is likely derived from Descartes (1644) 1984, §1.59 (see Kambouchner 1995, 185; Ndiaye 1991, 78–81). Descartes also endorses the intrinsic theory in this passage.
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